In [17]:
plt.scatter(y,x)
plt.scatter(y1,x1)
Out[17]:
<matplotlib.collections.PathCollection at 0x7f94822b7850>
SVM kernal Indepth Intution and Implementation
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
x = np.linspace(-5.0,5.0,100)
y = np.sqrt(10**2 - x**2)
y = np.hstack([y,-y])
x = np.hstack([x,-x])
x1 = np.linspace(-5.0,5.0,100)
y1 = np.sqrt(5**2 - x1**2)
y1 = np.hstack([y1,-y1])
x1 = np.hstack([x1,-x1])
plt.scatter(y,x)
plt.scatter(y1,x1)
<matplotlib.collections.PathCollection at 0x7f94822b7850>
For this we can not draw the bestfit line ,so we use SVM kernel trick to do !
df1 = pd.DataFrame(np.vstack([y,x]).T,columns=['X1','X2'])
df1['Y'] = 0
df2 = pd.DataFrame(np.vstack([y1,x1]).T,columns=['X1','X2'])
df2['Y']=1
df = df1.append(df2)
df.head()
| X1 | X2 | Y | |
|---|---|---|---|
| 0 | 8.660254 | -5.00000 | 0 |
| 1 | 8.717792 | -4.89899 | 0 |
| 2 | 8.773790 | -4.79798 | 0 |
| 3 | 8.828277 | -4.69697 | 0 |
| 4 | 8.881281 | -4.59596 | 0 |
Dividing the Independent and Dependent Data
X = df.iloc[:,:2] #x1,x2
y = df.Y #Y -> 0,1
Using train_test_split to train and test
from sklearn.model_selection import train_test_split
X_train, X_test , y_train ,y_test = train_test_split(X,y,test_size=0.25,random_state=0)
from sklearn.svm import SVC
from sklearn.metrics import accuracy_score
classifier = SVC(kernel="linear")
classifier.fit(X_train,y_train)
SVC(kernel='linear')
y_pred = classifier.predict(X_test)
accuracy_score(y_test, y_pred)
0.45
When we use linear Kenrnel we got .45 accuracy, Now we will train our model with kernel as poly (if we get low accuracy_score then go for other kernels)
------>Refer notes for clear undestanding<---------
k(x,y) = (x**T y + c)**d#we should fin components for poly
df['X1_Square'] = df['X1']**2
df['X2_Square'] = df['X2']**2
df['X1*X2'] = (df['X1']*df['X2'])
df.head()
| X1 | X2 | Y | X1_Square | X2_Square | X1*x2 | X1*X2 | |
|---|---|---|---|---|---|---|---|
| 0 | 8.660254 | -5.00000 | 0 | 75.000000 | 25.000000 | -43.301270 | -43.301270 |
| 1 | 8.717792 | -4.89899 | 0 | 75.999898 | 24.000102 | -42.708375 | -42.708375 |
| 2 | 8.773790 | -4.79798 | 0 | 76.979390 | 23.020610 | -42.096467 | -42.096467 |
| 3 | 8.828277 | -4.69697 | 0 | 77.938476 | 22.061524 | -41.466150 | -41.466150 |
| 4 | 8.881281 | -4.59596 | 0 | 78.877155 | 21.122845 | -40.818009 | -40.818009 |
Independent and dependent variables
X = df[['X1','X2','X1_Square','X2_Square','X1*X2']]
y = df['Y']
X_train, X_test , y_train ,y_test = train_test_split(X,y,test_size=0.25,random_state=0)
For 3D use plotly
!pip install plotly
Collecting plotly
Downloading plotly-5.5.0-py2.py3-none-any.whl (26.5 MB)
|████████████████████████████████| 26.5 MB 972 kB/s eta 0:00:01
Collecting tenacity>=6.2.0
Downloading tenacity-8.0.1-py3-none-any.whl (24 kB)
Requirement already satisfied: six in /Users/harikrishnareddy/opt/anaconda3/lib/python3.8/site-packages (from plotly) (1.15.0)
Installing collected packages: tenacity, plotly
Successfully installed plotly-5.5.0 tenacity-8.0.1
WARNING: You are using pip version 21.2.4; however, version 21.3.1 is available.
You should consider upgrading via the '/Users/harikrishnareddy/opt/anaconda3/bin/python -m pip install --upgrade pip' command.
import plotly.express as px
fig = px.scatter_3d(df,x='X1',y='X2',z='X1*X2',color='Y')
fig.show()
fig = px.scatter_3d(df,x='X1_Square',y='X2_Square',z='X1*X2',color='Y')
fig.show()
classifier = SVC(kernel="linear")
classifier.fit(X_train,y_train)
y_pred = classifier.predict(X_test)
accuracy_score(y_test, y_pred)
1.0